Literature Cited
A. Ya. Aleksandrov, “Solution of fundamental three-dimensional problems of the theory of elasticity for bodies of arbitrary form through numerical realization by the method of integral equations,” Dokl. Akad. Nauk SSSR,208, No. 2, 291–294 (1973).
É. S. Ventsel', V. G. Kobylinskii, and A. M. Levin, “Use of the method of regularization for the numerical solution of the problem of the bending of thin elastic plates,” Zh. Vychisl. Mat. Mat. Fiz.,24, No. 2, 323–328 (1984).
É. S. Ventsel' “Use of the method of compensating loads to design plates of complex form,” Dopov. Akad. Nauk Ukr. RSR Ser. A, No. 9, 43–45 (1980).
B. G. Korenev, “Method of compensating loads with application to problems of the equilibrium, vibration, and stability of slabs and membranes,” Prikl. Mat. Mekh.,4, No. 5–6, 61–72 (1940).
K. A. Kitover, “Use of special systems of biharmonic functions to solve certain problems of the theory of elasticity,” Prikl. Mat. Mekh.,26, No. 6, 739–748 (1952).
I. I. Kochetov and A. Kh. Rakhmatulina, “Solution of certain boudary-value problems for elliptic equations by means of first-order integral equations,” Dokl. Akad. Nauk SSSR,215, No. 3, 532–534 (1974).
V. M. Kulakov and V. M. Tolkachev, “Bending of plates of arbitrary contour,” Dokl. Akad. Nauk SSSR,230, No. 1, 56–59 (1976).
V. D. Kupradze and M. A. Aleksidze, “Method of functional equations for the approximate solution of certain boundary-value problems for elliptic equations by means of firstorder integral equations,” Dokl. Akad. Nauk SSSR,215, No. 3, 532–534 (1974).
A. M. Levin, “Calculation of a measure of the incompatibility of first-order operator equations,” Zh. Vychisl. Mat. Mat. Fiz.,26, No. 4, 499–507 (1986).
A. M. Levin, “Solution of biharmonic problems of the theory of elasticity in irregular regions by the method of first-order integral equations,” Summary of Documents of an All-Union Symposium: Method of Discretizing Singularities in Problems of Mathematical Physics. Khar'kov. Vyssh. Voen. Aviats. Inzh. Uch-Shche, Khar'kov (1985), pp. 63–65.
A. N. Tikhonov and V. Ya. Arsenin, Methods of Solving Ill-Conditioned Problems [in Russian], Nauka, Moscow (1986).
A. N. Tikhonov, I. I. Kochetov, and A. Kh. Pergament, “Some aspects of the use of the regularization method in solving boundary-value problems for elliptic equations, in: Gas and Wave Dynamics [in Russian], Mosk. Gos. Univ., Moscow (1979), pp. 29–34.
Ya. S. Uflyand, Integral Transforms in Problems of the Theory of Elasticity [in Russian], Nauka, Leningrad (1967).
Additional information
Kharkov Institute of Construction Engineering. Translated from Prikladnaya Mekhanika, Vol. 25, No. 12, pp. 101–107, December, 1989.
Rights and permissions
About this article
Cite this article
Ventsel', É.S., Levin, A.M. Solution of boundary-value problems of the theory of elasticity by numerical realization of the method of compensating loads. Soviet Applied Mechanics 25, 1259–1264 (1989). https://doi.org/10.1007/BF00887154
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00887154